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A228711
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G.f. A(x) satisfies: A(x)^4 = A(x^2)^2 + 8*x.
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3
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1, 2, -5, 22, -115, 646, -3822, 23496, -148368, 955822, -6256273, 41480668, -277954706, 1879118354, -12800031737, 87758481546, -605091552753, 4192829686338, -29180958305391, 203887504096188, -1429568781831693, 10055261467844862, -70929518958227340
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f. A(x) satisfies:
(1) A(x) = sqrt(1/G(x^2)^2 + 4*x*G(x^2)^2),
(2) sqrt(A(x^2)^2 + 4*x) = 1/G(x^4) + 2*x*G(x^4),
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EXAMPLE
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G.f.: A(x) = 1 + 2*x - 5*x^2 + 22*x^3 - 115*x^4 + 646*x^5 - 3822*x^6 +...
where A(x)^4 = A(x^2)^2 + 8*x as demonstrated by:
A(x)^2 = 1 + 4*x - 6*x^2 + 24*x^3 - 117*x^4 + 612*x^5 - 3426*x^6 + 20184*x^7 +...
A(x)^4 = 1 + 8*x + 4*x^2 - 6*x^4 + 24*x^6 - 117*x^8 + 612*x^10 - 3426*x^12 +...
G(x) = 1 + 3*x + 72*x^2 + 2307*x^3 + 86295*x^4 + 3513477*x^5 +...
and satisfies: sqrt(1/G(x^2)^2 + 4*x*G(x^2)^2) = A(x).
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PROG
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=(subst(A, x, x^2)^2+8*x+x*O(x^n))^(1/4)); polcoeff(A, n, x)}
for(n=0, 20, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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